The present invention relates to a system for the acceleration and deceleration utilizing digital control in a feedback control system.
The present invention is applicable to a numerical control machine tool, an automatic curve tracer, a magnetic disk memory drive system, et al.
First, a prior digital control system will be explained in accordance with FIG. 1, FIG. 2 and FIG. 3.
FIG. 1 is a block-diagram of a prior feedback type digital control system. In FIG. 1, the reference numeral 1 is a position register, the content of which shows the command position at which a table of a machine tool must be stopped. 2 is the first comparator which detects the difference between the command position indicated in the position register 1 and the present position of the table to be controlled. 3 is the second comparator for providing the difference between the output of said first comparator 2 and a velocity function which will be explained later. 4 is a motor drive, 5 is a motor for moving the table of the machine tool, 7 is the first detector for detecting the present position of the table, 6 is the second detector for detecting the velocity of the table, 8 is the matching circuit for providing the velocity function. The input command on paper tape is read into the position register 1, and the content of the position register indicates that the table is to be moved 0.001 mm for each pulse. When the content of the position register 1 is M, the table is moved by 0.001.times.M mm. Supposing that the frequency of the command pulse in the position register 1 is v.sub.i (t), which is the command velocity of the table, the output of the position register 1 is EQU .intg.v.sub.i (t)dt
and said output of the position register 1 indicates the goal position of the table. And supposing that v.sub.O is the velocity of the table, the present position of the table obtained from the first detector 7 is EQU .intg.v.sub.O (t)dt
The output of the second detector 6 is v.sub.O (t) and is connected to the input of the matching circuit 8, which provides the velocity function .tau.v.sub.O (t), where .tau. is a constant. The first comparator 2 provides the difference between the command position and the present position as follows. EQU .intg.v.sub.i (t)dt-.intg.v.sub.O (t)dt
And the second comparator 3 provides the difference between the output of the first comparator 2 (difference between the positions) and the velocity function as follows. EQU .intg.v.sub.i (t)dt-.intg.v.sub.O (t)dt-.tau.v.sub.O (t)
The motor drive 4 drives the motor 5 so that the output of the second comparator 3 becomes zero. Accordingly, the operation of the apparatus of FIG. 1 is shown in the formula (1). EQU .intg.v.sub.i (t)dt-.intg.v.sub.O (t)dt-.tau.v.sub.O (t)=0 (1)
It should be appreciated that the frequency of the command pulses relates to the velocity of the table, and the number of pulses relates to its length of travel.
FIG. 2 shows the block-diagram of the calculator for calculating the command position for the apparatus in FIG. 1. In FIG. 2, the reference numeral 9 is the input switch for initiating the start and/or stop of the movement of the table, 10 is a sign register for storing the sign (plus or minus) concerning the direction of travel, 11 is a control circuit for controlling the start and/or stop of the movement, 12 is a pulse generator the oscillating frequency of which is constant, 13 is an output circuit which provides the command pulse with the sign from the sign register 10, and the output circuit 13 is connected to the position register 1 in FIG. 1. 14 indicates the apparatus shown in FIG. 1.
When the switch 9 is turned on, the sign register 10 stores the sign of the movement, and the pulse generator 12 generates a train of pulses under the control of the control circuit 11, and the output circuit 13 provides the command pulse with the sign from the sign register 10 to the position register 1. When the switch 9 is turned off, the control circuit 11 causes the pulse generator 12 to stop. The frequency of the pulse generator 12 is equal to v.sub.i (t), accordingly, EQU v.sub.i (t)=F (2)
From the formulae (1) and (2), the formulae (3) and (4) are derived. EQU v.sub.O (t)=F(1=exp(-t/.tau.)) (3) EQU v.sub.O (t)=F exp(-t/.tau.) (4)
Formula (3) is available in acceleration period and the formula (4) is available during the deceleration period. The difference between the formulae (3) and (4) results from the difference of the initial values of the integral operation in solving the formulae (1) and (2).
The solid line in FIG. 3 shows the command velocity of the command pulses applied to the circuit 14, and it should be noted that the command velocity in the prior art is constant or flat. The dotted line in FIG. 3 shows the actual velocity of the table. As shown in FIG. 3, when the command velocity F is given, the table is accelerated gradually according to the formula (3) and reaches the final velocity F, and when the command velocity becomes zero the table is decelerated and gradually reaches zero velocity according to the formula (4). Since the command velocity in the prior art is constant or flat, the acceleration of the table is maximum at the start of its movement and the deceleration of the table is also maximum at the start of the deceleration period. It should be noted that the acceleration and/or deceleration is the differential coefficient of the velocity, and the power applied to the motor and/or the table is proportional to the acceleration and/or deceleration. Since there is an allowable maximum limit of acceleration and/or deceleration in each motor and/or table, the actual acceleration and/or the actual deceleration applied to the motor and/or the table must be smaller than the maximum limit, and therefore it takes a long time to reach constant velocity from the stationary condition, and/or to reach the zero velocity from the constant velocity. Further, the prior art has the further disadvantage that the power consumption of the motor is large since the acceleration time and/or deceleration time in the prior art is long.